Related papers: The Status of Cosmic Topology after Planck Data
What is the shape of space is a long-standing question in cosmology. In this talk I review recent advances in cosmic topology since it has entered a new era of experimental tests. High redshift surveys of astronomical sources and accurate…
Whether we live in a spatially finite universe, and what its shape and size may be, are among the fundamental long-standing questions in cosmology. These questions of topological nature have become particularly topical, given the wealth of…
Questions such as whether we live in a spatially finite universe, and what its shape and size may be, are among the fundamental open problems that high precision modern cosmology needs to resolve. These questions go beyond the scope of…
This review aims to cover the central aspects of current research in cosmic topology from a topological and observational perspective. Beginning with an overview of the basic concepts of cosmology, it is observed that though a determinant…
General relativity does not allow one to specify the topology of space, leaving the possibility that space is multiply rather than simply connected. We review the main mathematical properties of multiply connected spaces, and the different…
What is the shape of the Universe? Is it finite or infinite ? Is space multi-connected to create ghost images of faraway cosmic sources? After a "dark age" period, the field of cosmic topology has now become one of the major concerns in…
What is the shape of the Universe? Is it curved or flat, finite or infinite ? Is space "wrapped around" to create ghost images of faraway cosmic sources? We review how tessellations allow to build multiply-connected 3D Riemannian spaces…
We study the effect of global topology of the spatial geometry on the cosmic microwave background (CMB) for closed flat and closed hyperbolic models in which the spatial hypersurface is multiply connected. If the CMB temperature…
Is the universe finite or infinite, and what shape does it have? These fundamental questions, of which relatively little is known, are typically studied within the context of the standard model of cosmology where the universe is assumed to…
Is the Universe (a spatial section thereof) finite or infinite? Knowing the global geometry of a Friedmann-Lema\^{\i}tre (FL) universe requires knowing both its curvature and its topology. A flat or hyperbolic (``open'') FL universe is {\em…
Probing the geometry of the universe is one of the most important endevours in cosmology. Current observational data from the Cosmic Microwave Background anisotropy (CMB), galaxy surveys and type Ia supernovae (SNe Ia) strongly constrain…
``One could imagine that as a result of enormously extended astronomical experience, the entire universe consists of countless identical copies of our Milky Way, that the infinite space can be partitioned into cubes each containing an…
The measurements of CMB anisotropy have opened up a window for probing the global topology of the universe on length scales comparable to and beyond the Hubble radius. We have developed a new method for calculating the CMB anisotropy in…
The cosmic microwave background (CMB) is a unique probe of cosmological parameters and conditions. There is a connection between anisotropy in the CMB and the topology of the Universe. Adopting a universe with the topology of a 3-Torus, or…
The question of whether Cosmic Microwave Background (CMB) temperature and polarization data from Planck favor a spatially closed Universe with curvature parameter $\Omega_K<0$ has been the subject of recent intense discussions. Attempts to…
We analyse the anisotropy of the cosmic microwave background (CMB) in hyperbolic universes possessing a non-trivial topology with a fundamental cell having an infinitely long horn. The aim of this paper is twofold. On the one hand, we show…
Cosmology has come a long way from being based on a small number of observations to being a data-driven precision science. We discuss the questions "What is observable?", "What in the Universe is knowable?" and "What are the fundamental…
Cosmology's standard model posits an infinite flat universe forever expanding under the pressure of dark energy. First-year data from the Wilkinson Microwave Anisotropy Probe (WMAP) confirm this model to spectacular precision on all but the…
The standard method for observationally confirming the existence of a predicted finite topology of the universe involves searching for the repetition of the same finite or extended source in different directions. However, serious problems…
Given the wealth of increasingly accurate cosmological observations, especially the recent results from the WMAP, and the development of methods and strategies in the search for cosmic topology, it is reasonable to expect that we should be…